A box of mass `8 kg ` placed on a rough inclined plane of inclened `theta` its downward motion can be prevented by applying an upward pull `F` and it can be made to slide upward appliying a force `2F` .The coefficient of friction between the box and the inclined plane is

Options

A. `(1)/(3)tan theta`
B. `3tan theta`
C. `(1)/(2) tan theta`
D. `2 tan theta`

Explanation

Case (1) , `F+(1)+f=mg sin theta`
Case (2),`2F=f+mg sin theta`
`2(mg sintheta-f)=f+mg sin theta`
mg sin `theta=3f`
mg sin `theta=3mumg cos theta`
`mu=(1)/(3)tan theta`